Geodesic
Finite difference method for numerical solution to a boundary value problem for a mixed difference differential equation
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 3 (2000) no. 4, pp. 345-355 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A boundary value problem for a mixed linear difference differential equation in a bounded rectangular domain is considered. A difference scheme for the problem is constructed. Stability, existence, and uniqueness of the solution of arising system of difference equations is proved. Weak convergence of approximations to the generalized solution of the considered boundary value problem is also proved. 
@article{SJVM_2000_3_4_a5,
     author = {A. V. Kopylov},
     title = {Finite difference method for numerical solution to a~boundary value problem for a~mixed difference differential equation},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {345--355},
     year = {2000},
     volume = {3},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2000_3_4_a5/}
}
TY  - JOUR
AU  - A. V. Kopylov
TI  - Finite difference method for numerical solution to a boundary value problem for a mixed difference differential equation
JO  - Sibirskij žurnal vyčislitelʹnoj matematiki
PY  - 2000
SP  - 345
EP  - 355
VL  - 3
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/SJVM_2000_3_4_a5/
LA  - ru
ID  - SJVM_2000_3_4_a5
ER  - 
%0 Journal Article
%A A. V. Kopylov
%T Finite difference method for numerical solution to a boundary value problem for a mixed difference differential equation
%J Sibirskij žurnal vyčislitelʹnoj matematiki
%D 2000
%P 345-355
%V 3
%N 4
%U http://geodesic.mathdoc.fr/item/SJVM_2000_3_4_a5/
%G ru
%F SJVM_2000_3_4_a5
A. V. Kopylov. Finite difference method for numerical solution to a boundary value problem for a mixed difference differential equation. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 3 (2000) no. 4, pp. 345-355. http://geodesic.mathdoc.fr/item/SJVM_2000_3_4_a5/

[1] Kamenskii G. A., Myshkis A. D., “On the mixed type functional differential equations”, Nonlinear Analysis, TMA, 30:5 (1997), 2577–2584 | DOI | MR | Zbl

[2] Kamenskii G. A., “Boundary value problems for difference differential equations arising from variational problems”, Nonlinear Analysis, TMA, 18:8 (1992), 801–813 | DOI | MR

[3] Kamenskii G. A., “A review of the theory of mixed functional differential equations”, Problems of Nonlinear Analysis in Engineering Systems, 2:8 (1998), 1–16

[4] Ladyzhenskaya O. A., Smeshannaya zadacha dlya giperbolicheskogo uravneniya, Gostekhizdat, M., 1953

[5] Skubachevskii A. L., Elliptic functional differential equations and applications, Birkhäuser, Basel, Boston, Berlin, 1997 | MR | Zbl